Earthquake Research in China  2019, Vol. 33 Issue (4): 661-675     DOI: 10.19743/j.cnki.0891-4176.201904007
Magnetic Field Feedback Circuit for Geomagnetic Field Compensation Control
SHEN Xiaoyu, HU Xingxing, HE Zhaobo
Institute of Geophysics, China Earthquake Administration, Beijing 100081, China
Abstract: In the current state of geomagnetic instrument testing, some aspects of geomagnetic instrument performance are difficult to test in the laboratory. If laboratory test results are inadequate, the instrument will have multiple problems while operating in the field, where a geomagnetic instrumentation test platform with a stable natural magnetic field is critical. Here, the magnetic field feedback circuit for geomagnetic field compensation control is studied in detail. That is, the magnetic field measured by the feedback magnetic sensor and the required working magnetic field are compared as input to the system, and the electric signal is transmitted to the feedback coil through an analog circuit to form a closed loop control, which provides compensation to control the magnetic field. Compared with the existing magnetic shielding method, the analog control circuit can achieve the realization of any working magnetic field, and it is not limited to a null magnetic field. The experimental result shows that the system compensates the earth's magnetic field of 10, 000nT with an average error of 10.6nT and average compensation error of 0.106%, providing a high compensation accuracy. The system also shows high sensitivity and excellent stability. The feedback circuit has achieved effective compensation control for the earth's magnetic field.
Key words: Geomagnetic field     Compensation feedback     Analog circuit

INTRODUCTION

In geophysical exploration and seismic monitoring, the observation of geomagnetic fields is a critical research tool. Under normal circumstances, the average strength of the geomagnetic field is generally about 40, 000 to 60, 000nT, and the daily variation is on the order of tens of nanoteslas (Liu Jia et al., 2007; Hu Xingxing et al., 2010). To make accurate geophysical observations, it is particularly important to measure the geomagnetic field accurately and efficiently, which requires high-precision geomagnetic instruments for technical support. To ensure the accuracy of the test results, it is necessary to compensate for the earth's background magnetic field to make a sensor perform its characteristic evaluation in a reliable and stable magnetic environment.

At present, the geomagnetic instrument testing activity mainly has the following problems:

① due to the existence of daily changes in the environmental field, it is difficult to achieve a non-magnetic environment (Xing Li, 2015; Zhi Hongkui et al., 2016) and also obtain a large magnetic field uniform test area; ② some properties of geomagnetic instruments, such as orthogonality and temperature characteristics, are difficult to test in the laboratory; ③ because the traditional measurement process based on the station comparison method considers many uncertain factors, such as geomagnetic daily variation, temperature variation, and orientation deviation, the implementation process is very complicated; ④ the instruments of the geomagnetic network in China are calibrated according to laboratory test results without considering the actual running performance of the instrument in a natural geomagnetic field, so the practice of natural field operation has many problems, such as overly large temperature drift, unstable instrument baseline, inadequate orthogonality, substantial crosstalk between components, and inconsistencies in the data from two sets of instruments at one station. Therefore, it is important to establish a geomagnetic instrument test platform that can stably simulate natural magnetic fields.

The magnetic field feedback compensation circuit proposed in this paper can be applied to a natural field laboratory using a geomagnetic instrument detection platform. The compensation circuit can realize a near-zero magnetic environment. In addition, it can control the magnitude of the feedback amount to realize a stable magnetic field with any value and provide a reliable test environment for evaluating the performance of geomagnetic instruments.

1 MAGNETIC FIELD FEEDBACK CONTROL PRINCIPLE

To provide high-precision compensation parameters for a magnetic field feedback compensation system, it is necessary to generate a uniform magnetic field that is controllable in both size and direction. Generating a magnetic field with a current coil is currently the most accurate and convenient control method, and the strength of the generated magnetic field can be determined by the size of the coil and the intensity of the current passing through it. Studies have shown that when a straight metal wire passes current, a circular magnetic field is created around the wire. The field strength proportionally increases as the current throught the wire increases. According to the Biot-Savart Law, the magnitude of the magnetic field produced by a current element at any point P in space can be calculated by the following formula (Bell G. B. et al., 1989; Shi Xueliang, 2010; Restrepo-Álvarez A.F. et al., 2017):

 ${\rm{d}}\overrightarrow B = \frac{{{\mu _0}}}{{4{\rm{ \mathsf{ π} }}}}\frac{{I\overrightarrow {{\rm{d}}l} \times \overrightarrow {{e_R}} }}{{{R^2}}} = \frac{{{\mu _0}}}{{4{\rm{ \mathsf{ π} }}}}\frac{{I\overrightarrow {{\rm{d}}l} \times \overrightarrow R }}{{{R^3}}}$ (1)

where $\overrightarrow {{\rm{d}}\mathit{l}}$ is a tiny line element of the source current, $\overrightarrow {{e_R}}$ is the unit vector of the current element pointing to the field to be obtained, and μ0 is the vacuum permeability of 4π×10-7 T·m/A.

An identical pair of circular current-carrying coils are placed coaxially parallel to each other. When the coil pitch is a radius R, and currents of equal magnitude and direction are passed through the two coils, they form a pair of circular Helmholtz coils. According to the calculation results of the magnetic field superposition, the central axis region of the Helmholtz coil can be approximated as a uniform magnetic field within a certain range. This characteristic gives the Helmholtz coil a unique advantage in generating a uniform compensation magnetic field. If three pairs of such coils are combined in mutually orthogonal form, a uniform magnetic field in three directions can be generated, which can be used to simulate the three components X, Y and Z of the earth's magnetic field.

To provide appropriate placement and transportation during the experiment, a square Helmholtz coil is considered in this feedback circuit. Compared with the round Helmholtz coil, the spacing between the square Helmholtz coils is 0.5445 times the length of the coil to ensure a uniform magnetic field in the center of the assembly (Liu Kun et al., 2012; Tan Xi et al., 2012). In addition, the square Helmholtz coils of the same size have the advantages of lower total power and uniform magnetic field range than the circular Helmholtz coils (Dong Changhua et al., 2016; Zhang Jingwen et al., 2018). Taking into account the technical limitations of the actual coil fabrication process, the parameters of the designed Helmholtz coil are shown in Table 1, where each direction group contains two coils, a working coil and a compensation coil. The working coil is used to generate the magnetic field required for the measurement. Ideally, the magnetic field value obtained by the magnetic sensor is the working magnetic field. The compensation coil is used to, as much as possible, cancel the interference of the background magnetic field of the earth and ensure that the magnetic field to be tested is uniform and stable.

Table 1 Square Helmholtz coil group parameters

A schematic diagram of the feedback system is shown in Fig. 1.

 Fig. 1 Schematic diagram of the feedback system

The working coil produces the working magnetic field required to measure the performance of the instrument. The magnitude of the uniform magnetic field in the coil measured by the feedback sensor is compared with the predetermined value of the stable magnetic field. The obtained voltage difference signal is subjected to signal conditioning after filtering and proportional integration, and the voltage signal is converted into a current signal through the V/I module. The compensation magnetic field is generated by the compensation coil. Finally, the combined magnetic field of the coil's magnetic field vector and the geomagnetic field vector meets the different numerical requirements required for laboratory testing under the natural field of the geomagnetic instrument within the error tolerance.

2 SYSTEM DESIGN 2.1 System Power Supply Design

The feedback circuit operational amplifier designed in this study operates at ±15V DC. If a linear DC voltage source were used for power supply directly, it would have disadvantages such as low voltage stability and high frequency disturbance. To make the stability of the working voltage as good as possible and the circuit frequency interference as small as possible, the operational amplifier is powered by a combination of a linear power supply, which is the transformer voltage output, and a voltage regulator chip that supplies the actual voltage to the circuit board. Considering that the voltage drop of voltage regulator chips 7815 and 7915 is large, other types of voltage regulator chips on the market are used. After comparison and research, the LT1963AES8 regulator chip was found to have the advantages of low noise, low dropout voltage, small static current, fast transient response, and adjustable output voltage range. By setting an adjustment resistor, the voltage can be adjusted between 1.21V and 20V. The LT1175IS8 negative regulator, which is commonly used in battery-powered systems, has low linearity drop and adjustable output voltage. According to experiment, the output voltage is stable at 14.768V and -14.322V for a long time, and the variation is small. It has good stability and accuracy and plays a very good supporting role in the operation of the system, greatly reducing the impact of power supply fluctuations.

2.2 Subtraction Circuit Design

The fluxgate sensor measures the weak magnetic field by assuming a nonlinear relationship between the magnetic induction intensity and the magnetic field strength of the high-conducting magnetic core in the measured magnetic field under the saturation excitation of the alternating magnetic field (Guo Xin, 2015). According to the sensitivity of the selected sensor and the intensity range of the geomagnetic field in general, a range of 40, 000nT to 60, 000nT can be obtained, and the maximum output voltage of the magnetic sensor can be 8.4V.

The difference between the output voltage of the sensor and the voltage value of the set magnetic field is taken as the output of the subsequent signal processing. Considering that the voltage difference range is ±10V and the signal is almost a DC signal, an operational amplifier with good characteristics at low frequency and low voltage should be used. According to the manual of the OP07 operational amplifier, the input range of the OP07 is -14V to +14V, which has good noise characteristics at low frequencies, and has the advantages of low offset voltage, high precision, and low offset drift. In combination with the external resistor, the subtraction circuit shown in Fig. 2 is used as the overall input of the feedback compensation system.

 Fig. 2 Schematic diagram of the subtraction circuit
2.3 Signal Conditioning Design

Ideally, the output voltage of the sensor should be DC. However, in actual application, a fluxgate instrument with higher precision has unavoidable instrument noise. Meanwhile, there are also low-frequency noise sources that can produce large fluctuations in the experimental results; such sources include elevators, transformers, and pumps; and noises, from traffic for example; and alternating magnetic field. To suppress the noise of the sensor and the noise that may exist in the environment, it is necessary to process the signal by means of filtering, proportional integration, and similar methods. To simplify the circuit and reduce the additional introduced noise components, a filter with the Sallen-Key topology is used. This structure is the most common second-order active low-pass filter structure (Lin Huai et al., 2018), and its circuit is shown in Fig. 3.

 Fig. 3 Second-order filter with Sallen-Key structure

The circuit's input and output relationship is

 $\frac{{{V_2}}}{{{V_1}}} = \frac{1}{{{C_1}{C_2}{R_5}{R_6}{s^2} + {C_2}\left({{R_5} + {R_6}} \right)s + 1}}$ (2)

According to the standard form of the second-order system, the characteristic frequency of the filter is ${f_0} = \frac{1}{{2{\rm{ \mathsf{ π} }}\sqrt {{R_5}{R_6}{C_1}{C_2}} }}$. In consideration of the fluctuation frequency range of the geomagnetic field and low-frequency noise, the cutoff frequency is set to 10Hz. To ensure that the response time is as fast as possible and the filtering effect is as good as possible, and because existing market capacitors have fewer optional specifications, we set R5=R6 and C1=C2 and selected a 10kΩ resistor and 1μF capacitor.

2.4 Voltage-Controlled Constant Current Source Design

The difference voltage is subtracted from the voltage measured by the feedback sensor and the voltage of the set magnetic field. After a series of amplifications and signal processing, the voltage signal needs to be converted into the current signal required by the compensation coil to finally realize the ground magnetic field. For a magnetic field feedback control device composed of coils, the performance of the compensation depends not only on the coil design and fabrication process but also on the performance of the constant current source that supplies the coil; this is an extremely important aspect (Zhao Wuyi et al., 2012).

Assuming that the impedance of the coil does not change during operation, the stability of the compensation feedback device is mainly determined by the stability of the constant current source. Therefore, the voltage-controlled constant current source needs to have both a specific output capability and a relatively high stability. In addition, the voltage-controlled constant current source used for the feedback compensation circuit also needs to have high adjustment precision and excellent ripple stability (Qin Ling et al., 2010). In consideration of the above factors, a current source based on an operational amplifier is selected for the as because it has a small volume, high efficiency, and wide current adjustment range.

The voltage-current conversion circuit designed in this study is shown in Fig. 4. The voltage Ui is fed into the non-inverting input of the operational amplifier A1, and A1 controls the conduction level of the MOSFET tube and obtains the corresponding output current. The output current is sampled on the sampling resistor Rs, amplified, sent to the inverting input of A1, and compared with the input voltage. Then, the output current of the MOSFET tube is adjusted to achieve dynamic balance (Wang Yuling, 2006). Because a MOSFET is used as the adjustment tube, a large output current can be obtained, which is not limited to the small output current of the operational amplifier. In addition, the load comes from the drain of a MOSFET with high impedance, and the output impedance of the constant current source system is extremely high (Chen Kailiang et al., 1992; Zhang Cunkai, 2016).

 Fig. 4 Schematic diagram of voltage-controlled constant current source

According to the characteristics of the operational amplifier, when it operates in the linear region, the input terminal of the operational amplifier OP07 is approximately short-circuited, so the voltages of the non-inverting input and the inverting input of the operational amplifier can be considered equal. The operational amplifier operating in the linear region also satisfies the characteristic of the input end of the open circuit, and the current flowing to the non-inverting input terminal and the inverting input terminal is considered to be zero. In addition, the gate current of the MOSFET is almost zero. Therefore, the current flowing to the sampling resistor Rs and the load R1 can be regarded as the same. Then, we can obtain

 $\begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{V_{1 + }} = {V_{1 - }} = {V_i}\\ {V_{2 + }} = {V_{2 - }} = \frac{{{R_4}}}{{{R_3} + {R_4}}}{V_{{\rm{o2}}}} = \frac{{{R_4}}}{{{R_3} + {R_4}}}{V_i}\\ \;\;\;\;\;\;{i_L} = {i_s} = \frac{{{V_{2 + }}}}{{{R_s}}} = \frac{{{R_4}}}{{{R_3} + {R_4}}}\frac{{{V_i}}}{{{R_s}}} \end{array}$ (3)

Select the appropriate resistor, R4=R3, the above equation can be expressed as:

 ${i_L} = {i_s}=\frac{1}{2}\frac{{{V_i}}}{{{R_s}}}$ (4)

That is, in an ideal case, when the peripheral resistance satisfies the current condition, the output current is independent of the load magnitude of the circuit and is only proportional to the input voltage, forming a constant current source circuit.

In the square Helmholtz coil, the X-axis direction component of the uniform magnetic field region at the center of the coil can be expressed as:

 $B = \frac{{4{\mu _0}NI{l^2}}}{{\rm{ \mathsf{ π} }}}\frac{1}{{\left({{l^2} + {a^2}} \right)\sqrt {2{l^2} + {a^2}} }} = {K_B}I$ (5)

where the coil side length is 2l, the coil pitch is 2a (a=0.5445l), and KB is the coil constant. The magnetic field components in the Y and Z directions can be similarly expressed.

The current flowing through the compensation coil is equal to the current through the sampling resistor, and the magnetic field generated by the current of the compensation coil should ideally be superimposed onto the ground magnetic field component to achieve the desired stable value, thus obtaining

 $\frac{{0.14 \times \Delta B}}{{2{R_s}}} = \frac{{\Delta B}}{{{K_B}}}$ (6)

The above formula can be used to select a suitable sampling resistor that achieves the desired compensation effect.

3 CIRCUIT NOISE CALCULATION

The noise in the integrated operational amplifier circuit is voltage noise, current noise, resistance noise, and other interference noise. Because the compensation current should be DC ideally, even if there is interference, it is a low-frequency error signal. Therefore, in considering the noise of the operational amplifier, mainly low-frequency, or 1/f, noise is considered (Zhao Lei et al., 2016). The OP07 integrated operational amplifier has ultra-low offset voltage and does not require additional zeroing. It features high open-loop gain, low noise, and high accuracy for signal processing in sensors. The equivalent input voltage noise is 10.3nV/$\sqrt {{\rm{Hz}}}$ (f=10Hz), and the equivalent current noise is 0.32pA/$\sqrt {{\rm{Hz}}}$(f=10Hz). According to the voltage noise density map in the OP07 reference manual, the 1/f noise variation of OP07 is small, and it can be approximated as equal to the broadband noise in the noise calculation. In addition, resistance thermal noise is also a major source of circuit noise. In general, the noise of a 1kΩ resistor is about 4nV/$\sqrt {{\rm{Hz}}}$ at room temperature.

Depending on the selected component and design circuit, the noise sources are uncorrelated, and the noise that is converted to an output can be calculated as follows:

 $\begin{array}{l} {\rm{RTO = }}\sqrt {e_1^2 + e_2^2 + e_3^2 + \cdots } \\ {e_i} = \sqrt {e_{{\rm{nv}}}^2 + e_{{\rm{nv}}}^2 + {{\left({{i_{{\rm{nv}}}}{\mathit{R}_{{\rm{eq}}}}} \right)}^2}} \end{array}$ (7)

where env is the voltage noise density of the component, enr is the thermal noise of the resistor, and inv is the current noise density of the component. The component reference manual states that the noise of the output of the magnetic field feedback circuit is designed to be 88.75nV/Hz. According to the design of the second-order low-pass filter, and the order of the bandwidth correction, the effective value of the noise converted to an output is about 433.1nV, and the peak-to-peak value is about 2.599μV. That is, the magnetic field noise ≤0.019nT (peak-to-peak), which is in line with the accuracy requirements of the magnetic field feedback circuit design.

4 SOFTWARE SIMULATION

To verify the performance and compensation capability of the feedback circuit design, Multisim software was used to simulate the feedback circuit to complete the transient and steady-state analysis of the circuit. A function generator can be used to simulate the output of the actual sensor signal; the signal is output after the steps of circuit subtraction, filtering, and proportional integration; and the output result is analyzed using an oscilloscope or a baud meter. In the following discussion, the X-axis direction compensation feedback circuit is used as a representative for the simulation experiments, and feedback to the other two axis directions is similar. The results of the Bauer simulation test are shown in Fig. 5.

 Fig. 5 Bauer test simulation results

From Fig. 5, the cutoff frequency of the filter is approximately 10Hz; for an interference signal above the cutoff frequency, such as 100Hz, an attenuation of about -32.15dB can be produced. The result shows that the designed feedback branch can reduce the interference of high-frequency noise signals and alternating magnetic field signals on the circuit, and ensure the accuracy and reliability of the compensation magnetic field.

Voltages of different magnitudes are set separately to simulate different magnitudes of magnetic field compensation. The simulation results are shown in Table 2.

Table 2 Compensation at constant magnetic field (0Hz)

Table 2 shows the feedback compensation circuit has good compensation accuracy under a low-frequency sensor signal that is nearly constant. In the compensation range of 0-60, 000nT, under the condition of a steady DC magnetic field, at an average compensation as low as 10, 000nT, the ideal error is only 12.36nT, the error is only 0.1236%, and it has high compensation accuracy.

Considering that the system is for compensating dynamic changes in the geomagnetic field, an alternating voltage with a frequency of 3Hz is set to simulate actual geomagnetic field changes. We observed the dynamic compensation of the magnetic field through an oscilloscope, as shown in Fig. 6.

 Fig. 6 Schematic diagram of dynamic compensation waveform (red curve is the actual magnetic field waveform and green curve is the compensation magnetic field waveform)

From Fig. 6, through the adjustment control of the PID link of the circuit, the compensation circuit can closely track the magnetic field fluctuation in real time, provide compensation, and guarantee the stability of the uniform magnetic field region to be tested.

5 EXPERIMENTAL RESULTS AND ANALYSIS

Measurement of an actual X-axis coil provided a coil inductance L of 7.21μH and resistance R of 18Ω.

Due to the inductive effect of the coil, the frequency response characteristic will result in a time delay in the feedback signal. In severe cases, negative feedback may become positive feedback due to phase lag, resulting in circuit oscillations at certain frequencies. In this circuit design, the inductance L of the coil is much smaller than the resistance R. With phase frequency characteristics of $\varphi \left({j\omega } \right) = \arctan \frac{{7.21 \times {{10}^{ - 6}}\omega }}{{18}}$, the phase lag caused by the inductance at low frequencies is almost zero, or negligible.

Therefore, to conduct the experiment, an equivalent resistor can be used instead of the actual coil for operation. Fig. 7 is a physical diagram of the compensation circuit using the X-axis as an example.

 Fig. 7 Designed compensation system for the X-axis
5.1 System Frequency Response

In addition to the phase difference caused by the coil inductance effect in the feedback system, the filtering, PID control, and other links may cause a phase difference between the final compensated output signal and the original input signal. The system shown in Fig. 1 can be represented by the transfer function of Equation (8).

 $G\left(s \right) = \frac{{{G_0}\left(s \right)}}{{1 + {G_0}\left(s \right)H\left(s \right)}} = \frac{{{K_1}\frac{{\omega _{\rm{n}}^2}}{{{s^2} + 2\xi {\omega _{\rm{n}}}s + \omega _{\rm{n}}^2}}{K_p}\left({1 + \frac{1}{{{T_i}s}} + {T_{\rm{d}}}s} \right)}}{{1 + {K_1}\frac{{\omega _{\rm{n}}^2}}{{{s^2} + 2\xi {\omega _{\rm{n}}}s + \omega _{\rm{n}}^2}}{K_p}\left({1 + \frac{1}{{{T_i}s}} + {T_{\rm{d}}}s} \right)\frac{{{K_B}}}{{{R_f}}}}}$ (8)

The final frequency response of the circuit is shown in Fig. 7 based on the system design parameters.

It can be concluded that the system can maintain stability within the DC range at a compensation frequency of 10Hz, with a maximum phase difference of about 20°. In actual situations, a phase shifter can be used for phase adjustment to achieve the best compensation effect.

5.2 Actual Dynamic Compensation

In actual use, there are various frequencies of noise in the environment, and the experimental results of the system are shown in Figs. 9 and 10. Fig. 9 shows the AC signal (after subtraction of the DC portion).

 Fig. 8 System frequency response characteristics

 Fig. 9 Signal amplitude map (a) Input signal map. (b) Output signal map

 Fig. 10 Signal spectrum diagram (a)Input signal spectrum. (b) Output signal spectrum

It can be seen from these figures that the original input signal has more interference noise. Furthermore, the noise is obvious at 35Hz, outside the range of the background geomagnetic field fluctuation frequency. After adding the compensation circuit, the interference noise of the environmental field is significantly reduced, showing that the compensation system has a good attenuation effect.

5.3 Compensation Accuracy Analysis

Whether the magnetic field feedback control system can accurately compensate the geomagnetic field to achieve the required stable working magnetic field is the key problem to be solved by the geomagnetic instrument performance laboratory testing under a natural field. By measuring the magnitude of the magnetic field in the uniform region of the coil after the magnetic field is stabilized, and comparing it with the working magnetic field, the compensation accuracy of the system can be analyzed. In the actual experiment, the coil is replaced by the equivalent resistance. Thus, we measured the compensation current flowing through the load resistance, and the square Helmholtz coil group parameters were combined to obtain the magnitude of the compensation magnetic field and compare the result with the theoretical compensation value. The results are shown in Table 3.

Table 3 Actual compensation of magnetic field

We adjusted the signal voltage level and measured the value after the parameters of the feedback circuit were stable. It can be seen from Table 3 that under a small voltage signal, due to the low-frequency noise of the operational amplifier, the error of the compensation magnetic field is larger than that of the remaining voltage signals. However, the overall average compensation error is only 0.106%; that is, for an average compensation of a geomagnetic field of 10, 000nT, the error is 10.6nT, which meets the compensation accuracy required in practical applications.

The weak magnetic laboratory at the weak magnetic first-level metering station of the National Defense Science and Technology Industry of the 710 Research Institute of China Shipbuilding Industry Corporation has a typical magnetic field compensation range of ±100μT and magnetic field noise ≤0.1nT (peak-to-peak) (National Defense Technology Industry Weak Magnetic Level I Metering Station, http://www.weakm.com/products_detail/productId=83.html). Compared with the magnetic field compensation feedback circuit designed in this study, it has a wider compensation range and provides more accurate compensation, which can be applied to the performance testing of geomagnetic instruments.

5.4 Compensation Stability Analysis

The compensation current of the system is generated by the voltage-controlled constant current source module, and the stability of the compensation current directly determines the stability of the compensation magnetic field. As an example, we used the X-direction feedback circuit with an input signal voltage of 1.4742V, connected a 18Ω load resistance, and measured the compensation current value every 15s. The recorded data are shown in Table 4.

Table 4 Compensation current measurement data

During the testing time, the fluctuation of the compensation current is weak, which has little influence on the error caused by the experiment and meets the design requirements of the constant current source. In this case, the average compensation current is 144.227mA and the average fluctuation amplitude of the compensation current is 0.0924%, indicating a very high stability.

5.5 Compensation Sensitivity Analysis

Changes in the feedback system's compensation value during signal voltage changes reflects the sensitivity of the magnetic field feedback system. The original conditions are set to compensate a magnetic field of 40, 000nT with a signal voltage of 5.6V and compensation current of 556.444mA (the actual signal voltage is 5.683V). The experiment was carried out according to a 10% change in each signal voltage. After the magnetic field to be compensated was stabilized, the experimental data were recorded, as shown in Table 5.

Table 5 Compensation sensitivity record

According to the data in the table, the sensitivity of the feedback system is 97.863mA/V; that is, when the signal voltage changes by 1V, corresponding to a magnetic field change of 7, 143nT, and the compensation current varies accordingly by 97.863mA. The feedback system has a high sensitivity to input signal changes and can well realize the envisaged magnetic field feedback control function.

6 DISCUSSION AND CONCLUSION

In this study, a magnetic field feedback control circuit suitable for geomagnetic field compensation control was designed. This circuit has the advantages of small volume, wide compensation range, and lowcircuit noise. From experiments, the compensation of a geomagnetic field of 10, 000nT has an average error of 0.106%. The compensation accuracy is high, which satisfies the practical application requirements. The sensitivity of the feedback system is also high. When the signal voltage changes, the compensation current can be quickly changed, and the sensitivity is 97.863mA/V. In addition, the stability of the system is excellent. Measurement of the compensation current shows that it remains stable for a long time, with a fluctuation amplitude of 0.0924%. Therefore, the system can be applied to a natural field laboratory for compensating and controlling the geomagnetic field to construct the stable working magnetic field required for measurements by geomagnetic instruments.

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